How to Support or Reject a Null Hypothesis (for a Proportion: P-Value Method)
There are four main ways you’ll compute test values and reject or support a hypothesis: two ways are with proportions (i.e. percentages) and two are without (if you do not have a proportion, check out how to support/reject a null hypothesis). This how to shows you the steps to deciding whether to support or reject a null hypothesis, using the P-Value method.
Sample question: A researcher claims that more than 23% of community members go to church regularly. In a recent survey, 126 out of 420 people stated they went to church regularly. Is there enough evidence at α=0.05 to support this claim? Use the P-Value method.
Step 1: State the null hypothesis and the alternate hypothesis (“the claim”). Ho:p ≤ 0.23; H1:p>0.23 (claim)
If you aren’t sure how to do this, follow this link for How To State the Null and Alternate Hypothesis.
Step 2: Compute 
by dividing the number of positive respondents from the number in the random sample:
63/210 = 0.3.
Step 3:Find ‘p’ by converting the stated claim to a decimal:
23%=0.23.
Also, find ‘q’ by subtracting ‘p’ from 1: 1-0.23=0.77.
Step 4:Use the following formula to calculate your test value.
Click here if you want easy, step-by-step instructions for solving this formula.
If formulas confuse you, this is asking you to:
- Subtract p from(0.3-0.23=0.07). Set this number aside.
- Multiply p and q together, then divide by the number in the random sample. (0.23 x 0.77) / 420 = 0.00042
- Take the square root of your answer to 2. sqrt(0.1771)=0.0205
- Divide your answer to 1. by your answer in 3. 0.07/0.0205=3.41
*/ ?>
Step 5: Find the P-Value by looking up your answer from step 5 in the z-table. The z-value for 3.41 is .4997. Subtract from 0.500: 0.500-.4977=0.023.
Step 6: Compare your P-value to α. If the P-value is less, reject the null hypothesis. If the P-value is more, keep the null hypothesis. ).0.023<0.05, so we have enough evidence to reject the null hypothesis and accept the claim.
That’s it!
Related posts:
- How to Support or Reject a Null Hypothesis (for a Proportion)
- How to Support or Reject a Null Hypothesis (Using a P-Value)
- How to Support or Reject a Null Hypothesis
- How to State the Null Hypothesis in Statistics: Part Two
- How to State the Null Hypothesis in Statistics: Part One
Jennifer Thomas said:
Oct 18, 09 at 8:10 pmI’m having a really hard time with this. I keep rereading the steps and they make sense as I try the example you have provided, but as soon as I work the homework/test questions, I’m getting the answer wrong. I just can’t figure out where I’m going wrong. So far this site has been very helpful but I’m lost with this chapter.
Stephanie said:
Oct 19, 09 at 12:38 pmJennifer,
Email me the problem you are working on and I will take a look,
Stephanie
Angie Widdows said:
Oct 23, 09 at 9:51 amOne thing I do not understand is why Ho:p ≤ 0.23. I would think it would be greater than or equal to because the question states “A researcher claims that more than”. Great. I am confused on the first step…
Stephanie said:
Oct 23, 09 at 10:55 amAngie,
That’s because the null hypothesis (Ho:p ≤ 0.23)is the opposite of the claim.
Stephanie
Donna Allen said:
Oct 27, 09 at 2:03 pmI have to admit, this seemed a little overwhelming when first looking at all of the steps involved. But, your explanation was easy to follow and very helpful when doing the homework. Thank You.
Mary Johnson said:
Oct 27, 09 at 4:09 pmThis is confusing. Theses steps confused me more. I have been using “show me” on the assignments and trying to make sense of it.
Kalynn Grabau said:
Oct 30, 09 at 12:20 pmYeah, this stuff isn’t easy.
Lauren Schultz said:
Nov 02, 09 at 7:16 amTHIS HAS BY FAR BEEN MY MOST TRYING SECTION. AND ITS NOT EVEN THE WORK ITS THE LAST PART, THE WORDING. I GET SO LOST ON WETHER TO SUPPORT OR REJECT THE NULL. THE BOOK WORDS IT DIFF THAN THE HOMEWORK AND THE ‘HINT’ SECTION ON THE HOMEWORK IS NO HELP.
IF ANYONE CAN HELP PLZ LET ME KOW ID BE FOREVER GREATFUL!! :)
Donna Allen said:
Nov 02, 09 at 2:46 pmI agree that the wording is very confusing. I understand how to do the equations. But, the wording at the end of the problem is really confusing to me as well.
Rebecca Gamble said:
Nov 07, 09 at 11:37 pmI agree with everyone else I don’t undestand the wording or anything about these hypothesis.
Sarah M. Joyner said:
Nov 14, 09 at 9:26 amI find these hypothesis word problems very confusing. I have done multiples problems and everything matches up except for my “yes” or “no” response. Maybe I am not understanding how to answer when you reject the hypothesis. It does not make since that you would then say yes to the claim????
Jennifer Thomas said:
Nov 17, 09 at 5:59 pmI believe Step 3 should = .77 instead of .67
Stephanie said:
Nov 18, 09 at 5:03 amYou are correct :)
Thanks, Jennifer!
Angella Clarke said:
Nov 20, 09 at 2:08 pmFor some reason my calculations do not add up. I will just have to keep practicing.
Donna said:
Dec 06, 09 at 12:39 pmWhat happened to Step 4??
Vanessa DuBarry said:
Dec 10, 09 at 8:39 pmyes this had to be the hardest section, but any little help is good.
Alison Bryant said:
Mar 29, 10 at 7:09 pmI liked this one because it finally helped me to understand the P-value method, I was doing it backwards from how it should be understood in terms of Ha and Ho but now I understand.
rachel said:
Apr 05, 11 at 10:18 ami am confused why the The z-value for 3.41 is .4997. my table says the z value for 3.41 is .99996
Stephanie said:
Oct 27, 11 at 9:25 pmYou’re looking at the wrong z-table for the problem. There are two tables — one for the left of the curve and one for right of the curve.